Subgroups — C₆₇×#33144 #30712395

Order 17152.

858 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#470×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2855	C₂	1	2	yes	maximal
4	C₆₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1935	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1933	C₂	1	2	yes	maximal, complemented
10	C₆₇×#1894	C₂	1	2	yes	maximal
11	C₆₇×#1809	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
17	#470×C₆₇	—	2	4	no	—
18	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#103×C₆₇	C₂²	1	2	yes	—
22	C₂×#103×C₆₇	C₂²	1	2	yes	—
23	C₂×#103×C₆₇	C₂²	1	2	yes	—
24	C₄×M₁₆×C₆₇	—	2	4	no	—
25	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
29	#391×C₆₇	C₂²	1	2	yes	—
30	#391×C₆₇	C₂²	1	2	yes	—
31	#389×C₆₇	C₂²	1	2	yes	—
32	#389×C₆₇	C₂²	1	2	yes	—
33	#387×C₆₇	—	2	2	no	—
34	#387×C₆₇	—	2	2	no	—
35	#385×C₆₇	—	2	2	no	—
36	#381×C₆₇	—	2	2	no	—
37	#380×C₆₇	C₂²	1	2	yes	—
38	#340×C₆₇	C₂²	1	2	yes	—
39	#340×C₆₇	C₂²	1	2	yes	—
40	#340×C₆₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₆₇	D₄	1	2	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₆₇	—	2	2	no	—
45	C₂×Q₁₆×C₆₇	—	2	2	no	—
46	C₂×Q₁₆×C₆₇	—	2	2	no	—
47	C₂×M₁₆×C₆₇	—	2	2	no	—
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂×M₁₆×C₆₇	—	2	2	no	—
50	C₂×M₁₆×C₆₇	—	2	2	no	—
51	C₂×M₁₆×C₆₇	—	2	2	no	—
52	C₂×M₁₆×C₆₇	D₄	1	4	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
57	C₂²⋊Q₈×C₆₇	—	2	4	no	—
58	C₂²⋊Q₈×C₆₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
67	C₂×C₄²×C₆₇	—	2	2	no	—
68	C₂×C₄²×C₆₇	—	2	2	no	—
69	C₂×C₄²×C₆₇	D₄	1	2	yes	—
70	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
72	#107×C₆₇	—	2	2	no	—
73	#106×C₆₇	—	2	2	no	—
74	#106×C₆₇	—	2	2	no	—
75	#103×C₆₇	—	2	4	no	—
76	#103×C₆₇	—	2	4	no	—
77	#103×C₆₇	—	2	4	no	—
78	#97×C₆₇	—	2	2	no	—
79	#97×C₆₇	—	2	2	no	—
80	C₄×C₈×C₆₇	—	2	2	no	—
81	C₄×C₈×C₆₇	—	2	2	no	—
82	#95×C₆₇	—	2	2	no	—
83	#95×C₆₇	—	2	2	no	—
84	#95×C₆₇	—	2	2	no	—
85	#95×C₆₇	—	2	2	no	—
86	#95×C₆₇	—	2	2	no	—
87	#95×C₆₇	—	2	2	no	—
88	#95×C₆₇	—	2	2	no	—
89	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₆₇	—	2	2	no	—
91	C₂×Q₈×C₆₇	—	2	2	no	—
92	C₂×Q₈×C₆₇	—	2	2	no	—
93	C₂×Q₈×C₆₇	—	2	2	no	—
94	C₂×Q₈×C₆₇	—	2	2	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂²×C₄×C₆₇	—	2	1	no	—
97	C₂²×C₄×C₆₇	—	2	1	no	—
98	C₂²×C₄×C₆₇	—	2	1	no	—
99	C₂²×C₄×C₆₇	—	2	1	no	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	2	4	no	—
102	C₂²×C₄×C₆₇	—	2	2	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	C₂²×C₄×C₆₇	—	2	2	no	—
105	C₂²×C₄×C₆₇	—	2	2	no	—
106	C₂²×C₄×C₆₇	—	4	2	no	—
107	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₇	#41	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₆₇	—	4	4	no	—
114	M₁₆×C₆₇	—	2	8	no	—
115	M₁₆×C₆₇	—	2	8	no	—
116	C₂×C₈×C₆₇	—	2	1	no	—
117	C₂×C₈×C₆₇	—	2	1	no	—
118	C₂×C₈×C₆₇	—	2	1	no	—
119	C₂×C₈×C₆₇	—	2	1	no	—
120	C₂×C₈×C₆₇	—	2	1	no	—
121	C₂×C₈×C₆₇	—	2	1	no	—
122	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₆₇	#41	1	2	yes	—
125	C₂×C₈×C₆₇	#41	1	2	yes	—
126	C₂×C₈×C₆₇	#41	1	2	yes	—
127	C₂×C₈×C₆₇	#41	1	2	yes	—
128	C₄⋊C₄×C₆₇	—	2	2	no	—
129	C₄⋊C₄×C₆₇	—	2	2	no	—
130	C₄⋊C₄×C₆₇	—	2	2	no	—
131	C₄⋊C₄×C₆₇	—	2	2	no	—
132	C₄⋊C₄×C₆₇	—	2	2	no	—
133	C₄⋊C₄×C₆₇	—	2	2	no	—
134	C₄⋊C₄×C₆₇	—	4	4	no	—
135	C₄⋊C₄×C₆₇	—	4	4	no	—
136	C₄⋊C₄×C₆₇	—	4	4	no	—
137	C₂²⋊C₄×C₆₇	—	4	4	no	—
138	C₂²⋊C₄×C₆₇	—	4	4	no	—
139	C₄²×C₆₇	—	2	4	no	—
140	C₄²×C₆₇	—	2	1	no	—
141	C₄²×C₆₇	—	2	1	no	—
142	C₄²×C₆₇	—	2	1	no	—
143	C₄²×C₆₇	—	2	1	no	—
144	C₂³×C₆₇	—	2	1	no	—
145	C₂³×C₆₇	—	2	1	no	—
146	C₂³×C₆₇	—	2	2	no	—
147	C₂³×C₆₇	—	2	2	no	—
148	C₂³×C₆₇	#121	1	2	yes	—
149	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₆₇	—	4	2	no	—
151	Q₈×C₆₇	—	4	2	no	—
152	Q₈×C₆₇	—	4	2	no	—
153	Q₈×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	1	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	2	2	no	—
158	C₂×C₄×C₆₇	—	2	2	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	—	4	8	no	—
166	C₂×C₄×C₆₇	—	4	2	no	—
167	C₂×C₄×C₆₇	—	4	2	no	—
168	C₂×C₄×C₆₇	—	4	2	no	—
169	C₂×C₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	4	2	no	—
171	C₂×C₄×C₆₇	—	4	2	no	—
172	C₂×C₄×C₆₇	—	4	2	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	—	4	2	no	—
175	C₂×C₄×C₆₇	—	4	2	no	—
176	C₂×C₄×C₆₇	—	4	2	no	—
177	C₂×C₄×C₆₇	—	4	2	no	—
178	C₂×C₄×C₆₇	#121	1	2	yes	—
179	C₂×C₄×C₆₇	#137	1	4	yes	—
180	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
186	C₈×C₆₇	—	2	2	no	—
187	C₈×C₆₇	—	2	2	no	—
188	C₈×C₆₇	—	2	2	no	—
189	C₈×C₆₇	#123	1	4	yes	—
190	C₂²×C₆₇	—	2	2	no	—
191	C₂²×C₆₇	—	2	4	no	—
192	C₂²×C₆₇	—	4	2	no	—
193	C₂²×C₆₇	—	4	1	no	—
194	C₂²×C₆₇	—	4	1	no	—
195	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
196	C₂²×C₆₇	#532	1	1	yes	characteristic
197	C₂²×C₆₇	#532	1	1	yes	characteristic
198	C₂²×C₆₇	C₂×#137	1	2	yes	—
199	C₂²×C₆₇	#575	1	2	yes	—
200	C₄×C₆₇	—	2	2	no	—
201	C₄×C₆₇	—	2	4	no	—
202	C₄×C₆₇	—	4	2	no	—
203	C₄×C₆₇	—	8	2	no	—
204	C₄×C₆₇	—	8	2	no	—
205	C₄×C₆₇	—	8	2	no	—
206	C₄×C₆₇	—	8	2	no	—
207	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
208	C₄×C₆₇	#525	1	1	yes	characteristic
209	C₄×C₆₇	#529	1	1	yes	characteristic
210	C₄×C₆₇	#529	1	1	yes	characteristic
211	#33144	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂×C₆₇	—	4	2	no	—
213	C₂×C₆₇	#2854	1	1	yes	characteristic
214	C₂×C₆₇	#3056	1	2	yes	—
215	C₂×C₆₇	#3172	1	2	yes	—
216	C₂×C₆₇	#3183	1	1	yes	characteristic
217	C₂×C₆₇	#3185	1	1	yes	characteristic
218	C₂×#470	C₂×C₆₇	1	1	yes	characteristic
219	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic
220	#2855	C₂×C₆₇	1	2	yes	—
221	#1971	C₂×C₆₇	1	1	yes	characteristic, complemented
222	#1969	C₂×C₆₇	1	1	yes	characteristic, complemented
223	#1943	C₂×C₆₇	1	1	yes	characteristic, complemented
224	#1941	C₂×C₆₇	1	1	yes	characteristic, complemented
225	#1935	C₂×C₆₇	1	2	yes	complemented
226	#1933	C₂×C₆₇	1	2	yes	complemented
227	#1894	C₂×C₆₇	1	2	yes	—
228	#1809	C₂×C₆₇	1	1	yes	characteristic
229	C₆₇	#33144	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
232	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
234	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
235	#470	—	2	4	no	—
236	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
237	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
238	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
239	C₂×#103	C₂²×C₆₇	1	2	yes	—
240	C₂×#103	C₂²×C₆₇	1	2	yes	—
241	C₂×#103	C₂²×C₆₇	1	2	yes	—
242	C₄×M₁₆	—	2	4	no	—
243	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
244	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
247	#391	C₂²×C₆₇	1	2	yes	—
248	#391	C₂²×C₆₇	1	2	yes	—
249	#389	C₂²×C₆₇	1	2	yes	—
250	#389	C₂²×C₆₇	1	2	yes	—
251	#387	—	2	2	no	—
252	#387	—	2	2	no	—
253	#385	—	2	2	no	—
254	#381	—	2	2	no	—
255	#380	C₂²×C₆₇	1	2	yes	—
256	#340	C₂²×C₆₇	1	2	yes	—
257	#340	C₂²×C₆₇	1	2	yes	—
258	#340	C₂²×C₆₇	1	2	yes	—
259	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
260	C₂³×C₄	D₄×C₆₇	1	2	yes	—
261	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	D₄×C₆₇	1	4	yes	—
271	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂²⋊Q₈	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	D₄×C₆₇	1	2	yes	—
288	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
290	#107	—	2	2	no	—
291	#106	—	2	2	no	—
292	#106	—	2	2	no	—
293	#103	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	2	4	no	—
296	#97	—	2	2	no	—
297	#97	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
329	C₂²×C₄	#41×C₆₇	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
331	Q₁₆	—	4	4	no	—
332	M₁₆	—	2	8	no	—
333	M₁₆	—	2	8	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
342	C₂×C₈	#41×C₆₇	1	2	yes	—
343	C₂×C₈	#41×C₆₇	1	2	yes	—
344	C₂×C₈	#41×C₆₇	1	2	yes	—
345	C₂×C₈	#41×C₆₇	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	#121×C₆₇	1	2	yes	—
367	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	#121×C₆₇	1	2	yes	—
397	C₂×C₄	#137×C₆₇	1	4	yes	—
398	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	#123×C₆₇	1	4	yes	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
414	C₂²	#532×C₆₇	1	1	yes	characteristic
415	C₂²	#532×C₆₇	1	1	yes	characteristic
416	C₂²	C₂×#137×C₆₇	1	2	yes	—
417	C₂²	#575×C₆₇	1	2	yes	—
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	2	no	—
425	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
426	C₄	#525×C₆₇	1	1	yes	characteristic
427	C₄	#529×C₆₇	1	1	yes	characteristic
428	C₄	#529×C₆₇	1	1	yes	characteristic
429	C₂	—	4	2	no	—
430	C₂	C₆₇×#2854	1	1	yes	characteristic
431	C₂	C₆₇×#3056	1	2	yes	—
432	C₂	C₆₇×#3172	1	2	yes	—
433	C₂	C₆₇×#3183	1	1	yes	characteristic
434	C₂	C₆₇×#3185	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₆₇×#1971	C₂	semidirect
5. C₆₇×#1969	C₂	semidirect
6. C₆₇×#1943	C₂	semidirect
7. C₆₇×#1941	C₂	semidirect
8. C₆₇×#1935	C₂	semidirect
9. C₆₇×#1933	C₂	semidirect
211. #33144	C₆₇	direct (N × H)
221. #1971	C₂×C₆₇	semidirect
222. #1969	C₂×C₆₇	semidirect
223. #1943	C₂×C₆₇	semidirect
224. #1941	C₂×C₆₇	semidirect
225. #1935	C₂×C₆₇	semidirect
226. #1933	C₂×C₆₇	semidirect
229. C₆₇	#33144	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#470×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₆₇×#2855	2
C₆₇×#1971	2
C₆₇×#1969	2
C₆₇×#1943	2
C₆₇×#1941	2
C₆₇×#1935	2
C₆₇×#1933	2
C₆₇×#1894	2
C₆₇×#1809	2
#33144	67

Subgroups — C67×#33144 #30712395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33144 #30712395